User blog:MrLuk2000/The Average Star
Introduction In this blog I will be using Stellar Classication to determine what the "average star" is. Of course if you pulled a star, at random, out of the sky, it would be a M-Class Main Sequence most of the time. But on a large scale, say, 100 or more, you will pull other stars. If you destroyed 100 stars in one go, you would be destroying some K, G, F, and possibly A stars as well in that sample. So saying that the average is exclusively class M doesn't compensate enough. While the majority of the stars will be M, others will not, and thus need to be added into this hypothetical "average" star. The Calculation The following calculations will be finding the GBE of the stars. I will use the formula U = (3*G*M^2)/(r(5-n)), in which U is GBE in joules, G is the gravitational constant of 6.67408x10^-11, M is mass in kilograms, r is radius in meters, and n is the polytropic value attributed to the type of star. All the following stars have not yet left the main sequence, so they all receive a polytrope value of 3. I will be using two variables in addition to the results and the percentages. These variables are M and R. M is a solar mass, which is the mass of our Sun. R is a solar radii, which is the radius of our Sun. Class M Very common, and usually an orange-red coloration. Making up 76.45% of all stars, these stars range from 0.08–0.45, average 0.265 M, and have approximately 0.7 R. Average Class M: (3*(6.67408×10^-11)*((1.989×10^30)*0.265)^2)/(((6.957×10^8) × 0.7)*(5-3)) = 5.711x10^40 Percentage Compensation: (5.711x10^40)*0.7645 = 4.366x10^40 Class K Less common, and usually a light orange to orange-yellow coloration. Making up 12.1% of all stars, these stars range from 0.45-0.8, average 0.625, M, and range from 0.7-0.96, average 0.83, R. Average Class K: (3*(6.67408×10^-11)*((1.989x10^30)*0.625)^2)/(((6.957×10^8)*0.83)*(5-3)) = 2.679x10^41 Percentage Compensation: (2.679x10^41)*0.121 = 3.242x10^40 Class G Uncommon, and usually a light yellow to yellow-white in coloration; our Sun is Class G. Making up 7.6% of all stars, these stars range from 0.8-1.04, average 0.92, M, and range from 0.96-1.15, average 1.055, R. Average Class G: (3*(6.67408×10^-11)*((1.989×10^30)*0.92)^2)/(((6.957×10^8)*1.055)*(5-3)) = 4.567x10^41 Percentage Compensation: (4.567x10^41)*0.076 = 3.471x10^40 Class F Rare, and usually a yellow-white to white in coloration. Making up 3% of all stars, these stars range from 1.04-1.4, average 1.22, M, and range from 1.15-1.4, average 1.275, R. Average Class F: (3*(6.67408×10^-11)*((1.989×10^30)*1.22)^2)/(((6.957×10^8)×1.275)*(5-3)) = 6.646x10^41 Percentage Compensation: (6.646×10^41)*0.03 = 1.994x10^40 Class A Very rare, less than 1% of all stars, and usually a bright white to blue white in coloration. Making up 0.6% of all stars, these stars range from 1.4-2.1, average 1.75, M, and range from 1.4-1.8, average 1.6, R. Average Class A: (3*(6.67408×10^-11)*((1.989×10^30)*1.75)^2)/(((6.957×10^8)*1.6)*(5-3)) = 1.09x10^42 Percentage Compensation: (1.09x10^42)*0.006 = 6.54x10^39 Class B Extremely rare, and usually blue white to deep blue white in coloration. Making up only 0.13% of all stars, these stars range from 2.1-16, average 9.05, M, and range from 1.8-6.6, average 4.2, R. Average Class B: (3*(6.67408×10^-11)*((1.989×10^30)*9.05)^2)/(((6.957×10^8)*4.2)*(5-3)) = 1.11x10^43 Percentage Compensation: (1.11x10^43)*0.0013 = 1.443x10^40 Class O The largest main-sequence star and a nigh-literal 1-in-1 million, these ares are blue in coloration, Making up only a minuscule 0.00003% of all stars, these stars are approximately 16 M and approximately 6.6 R. Average Class O: (3*(6.67408×10^-11)*((1.989×10^30)*16)^2)/(((6.957×10^8)*6.6)*(5-3)) = 2.208x10^43 Percentage Compensation: 6.624x10^36 All Together Now to add all the percentage compensated values together to find the "average" star in the universe. Giants, brown/white dwarves, Wolf-rayet, and Neutron pulsar stars all excluded, since I can find no numbers on their prevalence in the universe. I must imagine they are insignificantly rare. Average Main Sequence Star GBE: (4.366×10^40)+(3.242×10^40)+(3.471×10^40)+(1.994×10^40)+(6.54×10^39)+(1.443×10^40)+(6.624×10^36) = 1.517x10^41 joules Final Tally Using the percentages of all the stars in the main sequence and the averages among them, we can determine that the average star in the sky will have an approximate GBE of 1.517x10^41 joules. So yes, even when taking into account the larger main sequence stars, the average star is still a fair bit easier to destroy than the Sun. Practical Significance While this will not generally apply to all star destroying feats, if a character destroys a random star, it is likely that, given averages, it will be an average Class M. That said, if one wants to use the true average, the main sequence average is more up to the task. This has the most significance for large numbers of stars in which the space between them remains unaffected. For example, when one creates or destroys all the stars in the universe/galaxy, using this number will be most appropriate. For example, here are some stellar amounts of stars that can be destroyed: 2,000 (Taken from Low-End Rose Cluster number, Warhammer 40,000):''' (1.517x10^41)*2000 = 3.034x10^44 joules, High 4-C, '''Large Star level 10,000: (1.517x10^41)*10000 = 1.517x10^45 joules, High 4-C, Large Star level+ 20,000 (Taken from High-End Rose Cluster Number, Warhammer 40,000):''' (1.517x10^41)*20000 = 3.034x10^45 joules, 4-B, '''Solar System level (High 4-C, Large Star level+ via Tier 4 Revisions) 100,000,000,000 (Approximate number of stars in the Milky Way Galaxy):''' (1.517x10^41*10^11 = 1.517x10^52 joules, 4-B, '''Solar System level 2x10^23 (Approximate number of stars in the Universe, assuming 2 trillion galaxies of equal star count to the Milky Way):''' 3.034x10^64 joules, 4-A, '''Multi-Solar System level *Note!: Take this one with a grain of salt; our galaxy is fairly large compared to the average galaxy. Synopsis It takes a lot of stars to equal the destructive power of unleashing a blast capable of wiping multiple out at once. In fact, there aren't even enough stars in the universe for all of their energy to destroy the entire Milky Way from edge to edge in one shot. So take "I made *X number* stars" with a grain of salt. Being able to make galaxies doesn't mean you can destroy them, and all matter in the space between them, in one shot. Category:Blog posts Category:Calculations